How do I extrude inwards instead of outwards?
First of all, you select the faces you want to extrude, then press E to extrude and simply drag inward, if you want to inset instead (second picture) press I and then scale by dragging with your mouse. Remember that instead of dragging, in both cases you can type a number so that you tell blender the "amount" of that action that you want.
See the pictures below for the differences.

Extruding inwards:


Insetting: